{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T16:13:04Z","timestamp":1762272784537,"version":"build-2065373602"},"reference-count":72,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,8,25]],"date-time":"2021-08-25T00:00:00Z","timestamp":1629849600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100004440","name":"Wellcome","doi-asserted-by":"publisher","award":["088130\/Z\/09\/Z","203147\/Z\/16\/Z"],"award-info":[{"award-number":["088130\/Z\/09\/Z","203147\/Z\/16\/Z"]}],"id":[{"id":"10.13039\/100004440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001866","name":"Fonds National de la Recherche Luxembourg","doi-asserted-by":"publisher","award":["13568875"],"award-info":[{"award-number":["13568875"]}],"id":[{"id":"10.13039\/501100001866","id-type":"DOI","asserted-by":"publisher"}]},{"name":"EPSRC Centre for Doctoral Training in Mathematics of Random Systems","award":["EP\/S023925\/1"],"award-info":[{"award-number":["EP\/S023925\/1"]}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-19-1-2556"],"award-info":[{"award-number":["N00014-19-1-2556"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000155","name":"Social Sciences and Humanities Research Council of Canada","doi-asserted-by":"publisher","award":["756-2020-0704"],"award-info":[{"award-number":["756-2020-0704"]}],"id":[{"id":"10.13039\/501100000155","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In theoretical biology, we are often interested in random dynamical systems\u2014like the brain\u2014that appear to model their environments. This can be formalized by appealing to the existence of a (possibly non-equilibrium) steady state, whose density preserves a conditional independence between a biological entity and its surroundings. From this perspective, the conditioning set, or Markov blanket, induces a form of vicarious synchrony between creature and world\u2014as if one were modelling the other. However, this results in an apparent paradox. If all conditional dependencies between a system and its surroundings depend upon the blanket, how do we account for the mnemonic capacity of living systems? It might appear that any shared dependence upon past blanket states violates the independence condition, as the variables on either side of the blanket now share information not available from the current blanket state. This paper aims to resolve this paradox, and to demonstrate that conditional independence does not preclude memory. Our argument rests upon drawing a distinction between the dependencies implied by a steady state density, and the density dynamics of the system conditioned upon its configuration at a previous time. The interesting question then becomes: What determines the length of time required for a stochastic system to \u2018forget\u2019 its initial conditions? We explore this question for an example system, whose steady state density possesses a Markov blanket, through simple numerical analyses. We conclude with a discussion of the relevance for memory in cognitive systems like us.<\/jats:p>","DOI":"10.3390\/e23091105","type":"journal-article","created":{"date-parts":[[2021,8,26]],"date-time":"2021-08-26T00:19:26Z","timestamp":1629937166000},"page":"1105","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Memory and Markov Blankets"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5108-5743","authenticated-orcid":false,"given":"Thomas","family":"Parr","sequence":"first","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London WC1N 3AR, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0126-4588","authenticated-orcid":false,"given":"Lancelot","family":"Da Costa","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London WC1N 3AR, UK"},{"name":"Department of Mathematics, Imperial College London, London SW7 2AZ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Conor","family":"Heins","sequence":"additional","affiliation":[{"name":"Department of Collective Behaviour, Max Planck Institute of Animal Behavior, D-78457 Konstanz, Germany"},{"name":"Centre for the Advanced Study of Collective Behaviour, University of Konstanz, D-78457 Konstanz, Germany"},{"name":"Department of Biology, University of Konstanz, D-78457 Konstanz, Germany"},{"name":"Nested Minds Network, London EC4A 3TW, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maxwell James D.","family":"Ramstead","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London WC1N 3AR, UK"},{"name":"Nested Minds Network, London EC4A 3TW, UK"},{"name":"Spatial Web Foundation, Los Angeles, CA 90016, USA"},{"name":"Division of Social and Transcultural Psychiatry, Department of Psychiatry, McGill University, Montreal, QC H3A 1A1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7984-8909","authenticated-orcid":false,"given":"Karl J.","family":"Friston","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London WC1N 3AR, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1152\/physrev.1929.9.3.399","article-title":"Organization for physiological homeostasis","volume":"9","author":"Cannon","year":"1929","journal-title":"Physiol. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"13029","DOI":"10.1073\/pnas.0506347102","article-title":"Structure of stochastic dynamics near fixed points","volume":"102","author":"Kwon","year":"2005","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"126001","DOI":"10.1088\/0034-4885\/75\/12\/126001","article-title":"Stochastic thermodynamics, fluctuation theorems and molecular machines","volume":"75","author":"Seifert","year":"2012","journal-title":"Rep. Prog. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"20190159","DOI":"10.1098\/rsta.2019.0159","article-title":"Markov blankets, information geometry and stochastic thermodynamics","volume":"378","author":"Parr","year":"2020","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_5","unstructured":"Friston, K. (2019). A free energy principle for a particular physics. arXiv."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann.","DOI":"10.1016\/B978-0-08-051489-5.50008-4"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ramstead, M.J., Friston, K.J., and Hip\u00f3lito, I. (2020). Is the free-energy principle a formal theory of semantics? From variational density dynamics to neural and phenotypic representations. Entropy, 22.","DOI":"10.3390\/e22080889"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1152\/jn.1989.61.2.331","article-title":"Mnemonic coding of visual space in the monkey\u2019s dorsolateral prefrontal cortex","volume":"61","author":"Funahashi","year":"1989","journal-title":"J. Neurophysiol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1016\/j.neuroimage.2008.10.008","article-title":"Population dynamics under the Laplace assumption","volume":"44","author":"Marreiros","year":"2009","journal-title":"NeuroImage"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Da Costa, L., Friston, K., Heins, C., and Pavliotis, G.A. (2021). Bayesian Mechanics for Stationary Processes. arXiv.","DOI":"10.1098\/rspa.2021.0518"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Pavliotis, G.A. (2014). Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations, Springer.","DOI":"10.1007\/978-1-4939-1323-7"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bakry, D., Gentil, I., and Ledoux, M. (2014). Analysis and Geometry of Markov Diffusion Operators, Springer International Publishing. [1st ed.].","DOI":"10.1007\/978-3-319-00227-9"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.plrev.2018.12.002","article-title":"Variational ecology and the physics of sentient systems","volume":"31","author":"Ramstead","year":"2019","journal-title":"Phys. Life Rev."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Smets, P. (1998). Graphical Models for Probabilistic and Causal Reasoning. Quantified Representation of Uncertainty and Imprecision, Springer.","DOI":"10.1007\/978-94-017-1735-9"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Risken, H. (1996). Fokker-Planck Equation. The Fokker-Planck Equation: Methods of Solution and Applications, Springer.","DOI":"10.1007\/978-3-642-61544-3"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.1109\/TVCG.2012.316","article-title":"The Helmholtz-Hodge Decomposition\u2014A Survey","volume":"19","author":"Bhatia","year":"2013","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_17","unstructured":"Barp, A., Takao, S., Betancourt, M., Arnaudon, A., and Girolami, M. (2021). A Unifying and Canonical Description of Measure-Preserving Diffusions. arXiv."},{"key":"ref_18","unstructured":"Kelly, P. (2021, August 24). Mechanics Lecture Notes: An Introduction to Solid Mechanics. Available online: http:\/\/homepages.engineering.auckland.ac.nz\/~pkel015\/SolidMechanicsBooks\/index.html."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"P07010","DOI":"10.1088\/1742-5468\/2012\/07\/P07010","article-title":"Beyond It\u00f4 versus Stratonovich","volume":"2012","author":"Yuan","year":"2012","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_20","unstructured":"Friston, K., Heins, C., Ueltzh\u00f6ffer, K., Da Costa, L., and Parr, T. Stochastic Chaos and Markov Blankets. Entropy, under review."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"035002","DOI":"10.1088\/1751-8121\/aaf190","article-title":"Characterising the nonequilibrium stationary states of Ornstein-Uhlenbeck processes","volume":"52","author":"Luck","year":"2019","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On Information and Sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_23","unstructured":"Duchi, J. (2021, August 24). Derivations for Linear Algebra and Optimization. Available online: https:\/\/web.stanford.edu\/~jduchi\/projects\/general_notes.pdf."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhang, F. (2005). The Schur Complement and Its Applications, Springer.","DOI":"10.1007\/b105056"},{"key":"ref_25","unstructured":"Bishop, C.M. (2006). Pattern Recognition and Machine Learning (Information Science and Statistics), Springer."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Kim, E.-J. (2018). Investigating Information Geometry in Classical and Quantum Systems through Information Length. Entropy, 20.","DOI":"10.3390\/e20080574"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"100602","DOI":"10.1103\/PhysRevLett.99.100602","article-title":"Measuring Thermodynamic Length","volume":"99","author":"Crooks","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Guel-Cortez, A.-J., and Kim, E.-J. (2020). Information Length Analysis of Linear Autonomous Stochastic Processes. Entropy, 22.","DOI":"10.3390\/e22111265"},{"key":"ref_29","unstructured":"Amari, S.-I. (2012). Differential-Geometrical Methods in Statistics, Springer Science & Business Media."},{"key":"ref_30","unstructured":"Ay, N. (2017). Information Geometry, Springer Berlin Heidelberg."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Da Costa, L., Parr, T., Sengupta, B., and Friston, K. (2021). Neural Dynamics under Active Inference: Plausibility and Efficiency of Information Processing. Entropy, 23.","DOI":"10.3390\/e23040454"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Amari, S.I. (2016). Information Geometry and Its Applications, Springer.","DOI":"10.1007\/978-4-431-55978-8"},{"key":"ref_33","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley-Interscience. [2nd ed.]."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.jtbi.2018.07.002","article-title":"Free-energy minimization in joint agent-environment systems: A niche construction perspective","volume":"455","author":"Bruineberg","year":"2018","journal-title":"J. Theor. Biol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/S0034-4877(16)30031-3","article-title":"Markov Chain Monte Carlo and Irreversibility","volume":"77","author":"Ottobre","year":"2016","journal-title":"Rep. Math. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.1088\/0951-7715\/28\/7\/2081","article-title":"Irreversible Langevin samplers and variance reduction: A large deviation approach","volume":"28","author":"Spiliopoulos","year":"2015","journal-title":"Nonlinearity"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.cortex.2015.03.025","article-title":"Active inference, communication and hermeneutics","volume":"68","author":"Friston","year":"2015","journal-title":"Cortex"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s00422-011-0424-z","article-title":"Action understanding and active inference","volume":"104","author":"Friston","year":"2011","journal-title":"Biol. Cybern."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Parr, T., Limanowski, J., Rawji, V., and Friston, K. (2021). The computational neurology of movement under active inference. Brain.","DOI":"10.1093\/brain\/awab085"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"070201","DOI":"10.1088\/0256-307X\/30\/7\/070201","article-title":"Dynamical Decomposition of Markov Processes without Detailed Balance","volume":"30","author":"Ao","year":"2013","journal-title":"Chin. Phys. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"20130481","DOI":"10.1098\/rstb.2013.0481","article-title":"The anatomy of choice: Dopamine and decision-making","volume":"369","author":"Friston","year":"2014","journal-title":"Philos. Trans. R. Soc. B Biol. Sci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.nlm.2004.06.005","article-title":"Memory systems of the brain: A brief history and current perspective","volume":"82","author":"Squire","year":"2004","journal-title":"Neurobiol. Learn. Mem."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"615626","DOI":"10.3389\/fncir.2020.615626","article-title":"A Diversity of Intrinsic Timescales Underlie Neural Computations","volume":"14","author":"Cavanagh","year":"2020","journal-title":"Front. Neural Circuits"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1113\/jphysiol.1973.sp010273","article-title":"Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path","volume":"232","author":"Bliss","year":"1973","journal-title":"J. Physiol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1162\/netn_a_00175","article-title":"Parcels and particles: Markov blankets in the brain","volume":"5","author":"Friston","year":"2021","journal-title":"Netw. Neurosci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1038\/nrn1201","article-title":"Working memory: Looking back and looking forward","volume":"4","author":"Baddeley","year":"2003","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Kiebel, S.J., Daunizeau, J., and Friston, K.J. (2008). A Hierarchy of Time-Scales and the Brain. PLoS Comput. Biol., 4.","DOI":"10.1371\/journal.pcbi.1000209"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2539","DOI":"10.1523\/JNEUROSCI.5487-07.2008","article-title":"A Hierarchy of Temporal Receptive Windows in Human Cortex","volume":"28","author":"Hasson","year":"2008","journal-title":"J. Neurosci."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"6","DOI":"10.3389\/neuro.09.006.2009","article-title":"Spatial selection of features within perceived and remembered objects","volume":"3","author":"Astle","year":"2009","journal-title":"Front. Hum. Neurosci."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2072","DOI":"10.1093\/cercor\/bhl116","article-title":"Attentional Modulation of Object Representations in Working Memory","volume":"17","author":"Lepsien","year":"2007","journal-title":"Cereb. Cortex"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1016\/j.neuropsychologia.2011.03.011","article-title":"Modulation of working-memory maintenance by directed attention","volume":"49","author":"Lepsien","year":"2011","journal-title":"Neuropsychologia"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1152\/jn.1973.36.1.61","article-title":"Unit activity in prefrontal cortex during delayed-response performance: Neuronal correlates of transient memory","volume":"36","author":"Fuster","year":"1973","journal-title":"J. Neurophysiol."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1038\/73975","article-title":"Prefrontal modulation of visual processing in humans","volume":"3","author":"Suwazono","year":"2000","journal-title":"Nat. Neurosci."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"14678","DOI":"10.1038\/s41598-017-15249-0","article-title":"Working memory, attention, and salience in active inference","volume":"7","author":"Parr","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1093\/cercor\/bhz118","article-title":"Prefrontal Computation as Active Inference","volume":"30","author":"Parr","year":"2019","journal-title":"Cereb. Cortex"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"2473","DOI":"10.1007\/s00213-019-05240-0","article-title":"The computational pharmacology of oculomotion","volume":"236","author":"Parr","year":"2019","journal-title":"Psychopharmacology"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1002\/(SICI)1098-1063(1998)8:3<205::AID-HIPO3>3.0.CO;2-I","article-title":"Episodic memory, semantic memory, and amnesia","volume":"8","author":"Squire","year":"1998","journal-title":"Hippocampus"},{"key":"ref_58","unstructured":"Anderson, J.R. (1976). Language, Memory, and Thought, Lawrence Erlbaum."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"e1430","DOI":"10.1002\/wcs.1430","article-title":"The development of motor behavior","volume":"8","author":"Adolph","year":"2017","journal-title":"Wiley Interdiscip. Rev. Cogn. Sci."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1080\/09541449208406181","article-title":"Procedural memory and neurological disease","volume":"4","author":"Soliveri","year":"1992","journal-title":"Eur. J. Cogn. Psychol."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1136\/jnnp.60.1.94","article-title":"Impaired procedural learning after damage to the left supplementary motor area (SMA)","volume":"60","author":"Ackermann","year":"1996","journal-title":"J. Neurol. Neurosurg. Psychiatry"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1753","DOI":"10.1093\/brain\/120.10.1753","article-title":"Cerebellum and procedural learning: Evidence from focal cerebellar lesions","volume":"120","author":"Molinari","year":"1997","journal-title":"Brain"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1152\/jn.00266.2007","article-title":"Sensory Prediction Errors Drive Cerebellum-Dependent Adaptation of Reaching","volume":"98","author":"Tseng","year":"2007","journal-title":"J. Neurophysiol."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"238104","DOI":"10.1103\/PhysRevLett.93.238104","article-title":"Reproducible Sequence Generation In Random Neural Ensembles","volume":"93","author":"Huerta","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"1812","DOI":"10.1162\/NECO_a_00863","article-title":"Active Inference and Learning in the Cerebellum","volume":"28","author":"Friston","year":"2016","journal-title":"Neural Comput."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1038\/nrn3827","article-title":"Time cells in the hippocampus: A new dimension for mapping memories","volume":"15","author":"Eichenbaum","year":"2014","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0006-8993(71)90358-1","article-title":"The hippocampus as a spatial map: Preliminary evidence from unit activity in the freely-moving rat","volume":"34","author":"Dostrovsky","year":"1971","journal-title":"Brain Res."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"509354","DOI":"10.3389\/frai.2020.509354","article-title":"Deep Active Inference and Scene Construction","volume":"3","author":"Heins","year":"2020","journal-title":"Front. Artif. Intell."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1007\/s00422-018-0785-7","article-title":"Deep active inference","volume":"112","year":"2018","journal-title":"Biol. Cybern."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.neubiorev.2017.04.009","article-title":"Deep temporal models and active inference","volume":"77","author":"Friston","year":"2017","journal-title":"Neurosci. Biobehav. Rev."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.tics.2004.02.004","article-title":"Upper processing stages of the perception\u2013action cycle","volume":"8","author":"Fuster","year":"2004","journal-title":"Trends Cogn. Sci."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"20130475","DOI":"10.1098\/rsif.2013.0475","article-title":"Life as we know it","volume":"10","author":"Friston","year":"2013","journal-title":"J. R. Soc. 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